A charge Q accumulates on the hollow metallic dome,of radius R,of a Van de Graaff generator.A probe measures the electric field strength at various points outside the sphere surface.If the probe is initially at a distance 2R from the sphere's center and then is moved to 3R,by what factor will the electric field reading change?

Question

Quizplus · Accepted Answer

The electric field due to a charged sphere at a point outside the sphere is given by:

E = kQ/r^2

where k is the Coulomb constant, Q is the charge on the sphere, and r is the distance from the center of the sphere to the point where the electric field is measured.

Initial reading of electric field (E1) at distance 2R from the center of the sphere is:

E1 = kQ/(2R)^2 = kQ/4R^2

Final reading of electric field (E2) at distance 3R from the center of the sphere is:

E2 = kQ/(3R)^2 = kQ/9R^2

Therefore, the factor by which the electric field reading changes is:

E2/E1 = (kQ/9R^2)/(kQ/4R^2) = 4/9

Simplifying, we get:

E2/E1 = (2/3)^2

Therefore, the answer is D), (2/3)

A Charge Q Accumulates on the Hollow Metallic Dome,of Radius